Studies of the Faint Galaxy Population

Recent observations of faint galaxies to $b_J \approx 28$ (e.g., Tyson
& Seitzer, 1988) show an excess in number density with respect to
simple flat universe models which incorporate K- and E-corrections but
unevolving luminosity functions.  Low $q_0,$ high $z_f$ models are
unfavoured by recent redshift measurements, but merging dominated
models and models involving differential evolution between bright and
faint galaxies or a new population of faint galaxies remain consistent
with the data and a flat universe.

In this thesis, observations and theory which contribute to our
understanding of these faint galaxy populations are described.  In
chapter 2 it is shown that $d_L,$ $dV/dz,$ $q_0,$ $z_f,$
the K- and E- corrections, $\phi^*,$ $M^*,$ $\alpha,$ and $\eta$ all
affect the faint number counts significantly, though not
independently, while the effect of $H_0$ is small.

A preliminary search for low surface brightness galaxies described in
Chapter 3 gave unpromising results, with a number density
to $z \approx 0.05$ of $n \approx (9\pm5) \times 10^{-3} h^3 Mpc^{-3},$ which
is about $7\pm 4\%$ of the number density for normal galaxies in the
corresponding magnitude range of $-14\ge M_B \ge -20$ represented in a
Schechter (1976) luminosity function with Efstathiou et al.'s (1988)
parametrisation.  Only about half of this low surface brightness
galaxy population is likely to be excess to that represented in the
Schechter function. The diameters of the population observed are
inconsistent with the hypothesis that they are the low-redshift
counterparts of the excess faint galaxies if the latter are assumed to
have a typical redshift of $z=0.25$ at $B \approx 24$ (as in Cowie
et al., 1991), though their magnitudes are consistent.

The angular two-point correlation function has been measured for a
field of faint galaxies to $v \approx 26.5$ at the South Galactic Pole.
The clustering of these faint galaxies is shown to be as low as that
found by Efstathiou et al. (1991), but Neuschaefer et al.'s (1991)
rising correlation function amplitudes as a function of median sample
magnitude are not found.  The former implies that clustering growth is
faster than it would be if clustering were fixed in proper
coordinates, i.e., $\epsilon > 0$ (eqn (4.25)). If for some reason we
have overestimated the uncertainties in our measurements, this result
would be even stronger.  Efstathiou et al. feel that $\epsilon > 0$ is
unlikely, so their favoured explanation is that the weakness in
clustering is due to the excess faint galaxies being an intrinsically
faint, low redshift, more weakly clustered than normal
population. N-body models used in this thesis do in fact predict
$\epsilon <0$ in agreement with Efstathiou et al. (Sect. 6.4), but
they also have a spatial correlation function amplitude which is far
lower than cosmological amplitudes, so this does not seriously
overrule the N-body results of Melott (1992) or Yoshii et al. (1993)
or the observational data of Warren et al. (1993), which all indicate
that $\epsilon > 0.$ Instead, it provides a constraint with which to
check future N-body simulations which are normalised with the
intention of having correlation functions at a cosmological scale.

Merger-induced evolutionary population synthesis (MIEPS) models are
defined and results shown in Chapters 5 and 6.
Apart from two caveats on spatial correlation function
normalisation and the size of the time interval between time stages
used, these models look like a good candidate for explaining the faint
counts, as expected. Burst-only star formation rate models are found
to be necessary, as exponentially decaying star formation rates do not
flatten the faint end of the mass function enough in converting it
into a luminosity function.  The burst-only models with initial
perturbation spectra as power law spectra with indices of $n=0$ and
$n=-2$ and detection thresholds of $r_{thresh}=5$ and
$r_{thresh}=1000$ were run.  The model with the most expected
parameters ($n=-2, r_{thresh}=1000$) gives a luminosity function
which roughly fits a Schechter function at $t \approx t_0,$ but gives
number counts which clearly don't fit the observations; while a model
with less likely parameters ($n=0, r_{thresh}=5$) gives a luminosity
function which has the slope of a Schechter function and fits a
Schechter function overall if the compensatory factor $A$ is allowed,
in which case the number counts fit reasonably well to the
observations apart from the faint end.  An increase in time resolution
of the N-body output is likely to improve the fit of the latter model
more than that of the former.
 
Hence, these models favour a white-noise-like initial perturbation
spectrum ($n \approx 0$) with a low detection threshold
($r_{thresh} \approx 5$) and a correction factor $A=7$ as a candidate
for explaining the excess of faint galaxies; while a CDM-like spectrum
on these scales ($n \approx -2$) appears less likely.

An additional result from the N-body galaxy evolutionary modelling is
that the individual merger rates can be very different from the
average merger rates and that the fraction of mass coming from
accretion can be quite high.  For example, for the $n=0,
r_{thresh} = 5$ model, the mean number of peaks which collapse from the
intergalactic medium at any time stage and end up in a peak at the
final time stage is $7.4$, while the standard deviation in this
quantity is $20.7$. While this result is likely to quantitatively
change with the new N-body simulations, qualitatively it is unlikely
to.